Embedded-Atom Potentials

An extended discussion on embedded-atom potentials necessary for MD calculations can also be found (49). 

Dislocation core structures of (100), (110) and (111) dislocations in NiAl have been studied by molecular statics calculations using a new many-body embedded atom potential. They... 

This concept of metallic cohesion as arising from embedding ions in a gas of free electrons suggests that the binding energy of a collection of atoms with position vectors Rf may be approximated in the form of an embedded atom potential, namely... 

Embedded atom potentials have been extensively used for performing atomistic simulations of point, line and planar defects in metals and alloys (e.g. Vitek and Srolovitz 1989). The pair potential ( ), atomic charge density pBtom(r), and embedding function F(p) are usually fitted to reproduce the known equilibrium atomic volume, elastic moduli, and ground state structure of the perfect defect-free lattice. However, the prediction of ground state structure, especially the competition between the common metallic structure types fee, bcc, and hep, requires a more careful treatment of the pair potential contribution ( ) than that provided by the semiempirical embedded atom potential. This is considered in the next chapter. 

Thus, the total binding energy per atom of a NFE metal can be expressed in a physically transparent form, as the sum of a volume-dependent contribution and a pair-potential contribution in a manner that is reminiscent of the semi-empirical embedded atom potential of eqn (5.68). It follows from eqs (6.59M6.72) that... 

M.I. Baskes et al Semiempirical modified embedded-atom potentials for silicon and germanium. Physl. Rev. B 40, 6085-6100 (1989)... 

In our own work,33 that we here shall discuss briefly, we used the embedded-atom potential together with the Aufbau/Abbau method of Section 2.8 in optimizing the structure. The stability function, A2E(N), Eq. (50), is shown in Figure 18. It shows a set of peaks that correspond to particularly stable clusters. It is interesting to notice that if one instead studies the total-energy difference... 

Baskes. M. I.. Modified embedded-atom potentials for cubic materials and impurities. Phys. Rev. B 46, 2727-2742 (1992). 

This so-called embedded atom potential consists of two terms. The first term is a two-body potential that represents the repulsion between the ion and the rest of the ions in the system. The second term is a many-body function that represents the energy to embed an atom in the position i, where there is an electron density p that comes from the linear superposition of spherically averaged atomic electron densities. 

Fig. 1.9. Dislocation core in A1 as seen experimentally using high-resolution transmission electron microscopy (a) and image simulation of results of atomistic simulation using embedded-atom potentials (b) (adapted from Mills et al. (1994)).

Fig. 5.14. Energy as a function of volumetric strain as computed using atomic-scale analysis in terms of embedded-atom potentials (courtesy of D. Pawaskar). The atomistic result is compared with the quadratic fit like that suggested in eqn (5.93).

Using the Cauchy-Born rule in conjunction with the Johnson embedded-atom potential, compute the energy of a shearing deformation on (111) planes in the [110] direction. Show that the energy has the form given in fig. 2.14. 

Schwoebel Barrier on fee (111) Surfaces Using the Johnson embedded atom potential introduced in chap. 4, compute the energetics of an adatom in the vicinity of a step and derive results analogous to those given in fig. 11.2. 

Both the Finnis-Sinclair and the embedded-atom potentials (together with others that we have not considered here) can be represented using a very similar functional form. However, it is important to realise that they differ in the way that they connect to the first-principles, quantum mechanical model of bonding. They also differ in the procedures used to parametrise the models, so that different parametrisations may be reported for the same material. 

Embedded Atom potentials [95]. These are designed for simulations of metals and incorporate a simplified approximation of the local electron cloud density due to the presence of neighboring atoms. 

The Tight-Binding Model and Embedded-Atom Potentials... 

An elemental metal is described by three functions 0(R),p R) and F(p), while a binary system A-B requires seven functions 0aa, ab. bb. Pa[R), Pb(R), Fa(p), Fb(p). Over the past two decades the embedded-atom potentials have been constructed for many metals and a number of binary systems. EAM functions are usually defined by analytical expressions. The pair-interaction and electron-density functions are normally forced to vanish together with several higher derivatives at a cutoff radius R. Typically, Rc covers 3-5 coordination shells. 

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